Possible way to have a different background than the HDRI background?
If you want to use the HDRi to light the scene, but want a transparent background to be composited later with the background, or want to blur the HDR or maybe replace it all together, enable film transparent.



Then you can use alpha over to combine the scene with any other image.



If you enable the Environment output for the render layers, you can also make the HDRi background avalable to be used it as a different element in the compositor.



The Env socket contains the information from the background so that it can be manipulated any way you want.




  Update. To do this in Eevee in 2.8


Just enable Film>Alpha>Transparent.

Then on the compositor use Alpha over to mix over the background you want to use.



Alternatively you can use a background for the world that is only seen by the camera and not by other rays, therefore not contributing to the lights, reflectons,etc.

Set two different Environment background shaders and use the Is Camera Ray from a Light Path node to control the shader mix.